The field of the invention relates generally to the simulation of electrical circuits, and more particularly to the time domain, steady-state simulation of circuits including frequency-dependent linear components.
An important step in the process of designing and constructing radio frequency (RF) integrated circuits is simulation. Indeed, simulation can and should be performed during the design process to ensure that the ultimate goals are achievable and will be realized by the finished product. For example, simulation should be used in the design of the RF integrated circuits that are at the heart of various wireless products such as cellular telephones. Moreover, the exploding demand for high performance wireless products has increased interest in efficient and accurate simulation techniques for RF integrated circuits.
A wireless communications device is comprised of a transmitter and a receiver. Each of these components can be separated into a baseband section and an RF section. The baseband section consists of the range of transmission and reception frequencies. The RF section of the transmitter converts the processed baseband signal to the assigned channel and then sends the signal out. The RF section of the receiver receives the signal and converts it to a baseband signal.
A transmitter should be made so that a minimal amount of energy is used to transmit a standard amount of energy, while not interfering with any transceivers operating on neighboring channels. A receiver should be made so that it can recover small signals accurately, without interference from other channels, while using a minimal amount of energy.
Unfortunately, RF circuits—which are generally constructed using such components as amplifiers, filters, mixers, and oscillators—do not lend themselves to conventional simulation techniques for several reasons.
First, RF circuits have narrowband signals that ride on modulated carriers. For example, cellular telephones have a modulated bandwidth in the range of tens to hundreds of kHz—a relatively low frequency modulation signal range—that rides on a high frequency carrier signal in the range of a few GHz. Since standard simulators, such as SPICE class simulators, use transient analysis to predict the non-linear behavior of a circuit, and since this type of analysis is expensive to use to resolve low modulation frequencies in the presence of a high carrier frequency, these simulators are not well suited to RF circuit simulation.
Second, RF circuits such as mixers exhibit non-linear behavior in response to an additional, large periodic signal known as the LO. This behavior arises because these circuits translate signals from one frequency to another. Unfortunately, standard simulators perform small-signal analyses, such as are needed to predict circuit noise, by linearizing a non-linear, time-invariant circuit about a constant operating point. Therefore, they produce a linear, time-invariant representation that is unable to exhibit the frequency translation effects that are needed to correctly predict noise and gain.
Third, many linear passive components, which play a significant role in circuit behavior, are modeled in the frequency domain using analytic expressions or S-parameter tables. Distributed components are described using partial differential equations, and hence lend themselves to frequency domain analysis. In contrast, time domain simulators are structured to solve systems of first-order, ordinary differential equations. Therefore, they are of limited use by themselves in modeling distributed components.
Thus, RF circuit simulation is difficult because RF circuits typically contain signals with multiple timescale properties, since the data and carrier signals in a system are usually separated in frequency by several orders of magnitude.
When a narrowband signal is passed through a non-linear circuit, it produces a broadband signal with a relatively sparse spectrum. Special purpose RF simulators exploit this sparsity of spectrum in order to make the necessary computations tractable. For example, instead of performing a long transient analysis of a circuit driven by a periodic source, the simulator may seek to find the steady-state directly.
Circuit simulation methods ultimately solve circuit equations, i.e., systems of differential equations. They do this in either the time domain or the frequency domain.
Time domain simulation methods discretize circuit equations using finite difference methods such as the second-order Gear method. The advantage of using time domain methods is that they can select time points based on localized error estimates. As a result, they can easily handle strongly nonlinear phenomena and sharp transitions in circuit waveforms.
Frequency domain simulation methods, such as the harmonic balance method, are popular for RF circuit simulation as they have the advantage of attaining spectral accuracy for smooth waveforms. In addition, the development of matrix-free Krylov-subspace algorithms has made dedicated RF simulation tools even more popular as they can now be used to analyze circuits with thousands of devices.
RF communication circuits often contain components—particularly passive components such as transmission lines, integrated inductors, and SAW filters—where distributed effects are important. Distributed components are components that are not conveniently described by a finite-dimensional, or “lumped,” state-space model because they have an infinite-dimensional state space. The term “distributed component” is used to refer to any component more conveniently described by a frequency domain or convolutional representation. Frequency domain methods have the advantage that they can be used with equal ease to simulate either distributed devices or lumped devices.
In contrast to frequency domain techniques, which have no more difficulty simulating distributed devices than lumped devices, a significant drawback of time domain methods heretofore, is that the simulation of distributed or passive components is much more difficult for them. However, since time domain methods do have the distinct advantage previously noted—that they can select time points based on localized error estimates—it is desirable to use them in simulating distributed devices, in spite of the difficulties associated with their implementation.
There are generally two approaches to using time domain methods in simulating distributed devices. The first approach is to apply a model generation tool to generate finite-dimensional, state-space models for those components. These state-space models are then easily simulated in the time domain. The second approach is to compute, the impulse response of the distributed element, and then apply a convolution approach at each time step to obtain the time domain response of the element. In transient analysis one may use a direct convolution approach to simulate these components without significant difficulty.
In the more general setting of RF circuit simulation, however, such as when using periodic steady-state analysis via shooting-Newton methods, problems arise due to the fact that the distributed components have an infinite-dimensional state space.
First it is not sufficient to calculate the state of the circuit at a single point of the periodic time interval in order to describe the periodic steady-state. Instead, the distributed state of the devices is computed. This in turn implies that the sensitivity calculation in the shooting methods involves more than the two end points of the periodic interval.
Second, the distributed components destroy the block-banded structure of the Jacobian that is exploited in preconditioner computation.
Thus, each type of method—time domain or frequency domain—has strengths that makes it useful in simulation. However, when used alone, each method has weaknesses that limit its applicability to simulating RF circuits efficiently and effectively. It is therefore highly desirable to have a way to combine the strengths of these methods and simultaneously overcome their individual weaknesses. In particular, it would be very useful to have a way to simulate an RF circuit so that on the one hand steady-state time domain analysis can be applied, while on the other hand the distributed passive components of the circuit—i.e., those with an infinite dimensional state space, or a frequency domain description,—can also be simulated.
The present invention solves these problems by providing a method, an apparatus, and a computer program product for simulating a radio frequency (RF) circuit. Various embodiments use a hybrid frequency-time approach to RF simulation. In particular, these embodiments can be used to simulate an RF circuit so that on the one hand steady-state time domain analysis can be applied, while on the other hand the distributed passive components of the circuit—e.g., those with an infinite dimensional state space, or a frequency domain description,—can also be simulated.